Nonlinear dynamics of the magnetization of ferromagnets and motion of a generalized solid with flow group

Arnol'd proposed an approach to investigation of the hydrodynamics of an ideal fluid based on the introduction of the group of diffeomorphisms of the flow region as configuration space. An analogous investigation was made of a generalized solid, the part of the configuration space being played by a certain Lie group. The motions were described by the geodesics of invariant metrics on the corresponding Lie groups [1]. The aim of the present paper is to apply such an approach to the problem of the nonlinear dynamics of the magnetization of ferromagnets.